God had a better way: Jesus Christ.
"For they being ignorant of God’s righteousness, and seeking to establish their own righteousness, have not submitted to the righteousness of God. For Christ is the end of the law for righteousness to everyone who believes." (10:3-4)
Christ was righteous in every point. 100.000% Righteous. So what does God do? He sends Jesus to die our death, so that we may receive His righteous life, by faith.
For as by one man's disobedience many were made sinners, so also by one Man's obedience many will be made righteous. (Rom. 5:19)
The righteousness that comes by faith isn't inferior. It still passes God's impeccable eyesight. But it has a different testimony. (10:6-9) It doesn't say "Who's going to get Christ down from heaven?" or "Who's going to bring Christ up from the dead?" None of those actions are necessary.
"But what does it [the righteousness of faith] say? “The word is near you, in your mouth and in your heart” (that is, the word of faith which we preach): that if you confess with your mouth the Lord Jesus and believe in your heart that God has raised Him from the dead, you will be saved." (10:8-9) The word is near you... present tense! It's already here! And I can never read "word" without thinking John 1; "And the Word was made flesh, and dwelt among us" (Jn. 1:14a) - Jesus!
We have some friends who are Mormon. Recently we visited their church when their 8-year-old daughter got baptized. Of course we were being really watchful to discern the substance of their doctrine. A lot of it is very similar to Christianity, so unless you know your Bible, it would be extremely easy to just go along with it. One of the things we noticed was how, although they recognize Jesus' death being an "atonement" for our sin, they emphasize the need to "do the best that you can" after you believe, as though we could repay God. Oh, thank you Jesus that your righteousness was sufficient, because I sure don't have any apart from you! And, you are in my heart. You haven't left me the same!